Nashota pays $30 each month on a credit card that charges 1.4% interest monthly. She has a balance of $450. The balance at the beginning of the month is given by the following function that is defined recursively. Find the balance at the beginning of the fifth month

To answer, we project the current balance to future worth.

FV = ($450) x (1 + 0.014) ^5

FV = $482.40

Also, we convert the monthly amount to future worth by the equation,

FV = M x ((1 + r) ^n - 1) / r)

Substituting,

FV = ($30) x (1 + 0.014) ^5 - 1) / 0.014)

FV = $152.3

Subtracting the calculated values,

Balance = $482.40 - $152.3

Balance = $328.14